All my objects became non-selectable
One option is to use shortcuts in the Outliner editor - V for visibility of the objects, S - for selectability and R for renderability. Note that mouse has to be over the Outliner editor while using the shortcuts.


Open the Outliner. You need to point to Blender which objects' settings you want to edit. As they are unselectable, press A which will create blue overlay over the objects and will select them for the Outliner actions.
Press the shortcut for desired operation, in the case of the question - S for selectability.




Note that this is toggle, so it will invert current state of the adjacent property; if object-A was unselectable and object-B was selectable, objectA will become selectable and objectB the other way around.